There has been many researches on a method for producing an α,β-unsaturated carboxylic acid through liquid-phase oxidation of an olefin or an α,β-unsaturated aldehyde with molecular oxygen by using a noble metal-containing catalyst. For example, in Patent Documents 1 to 4, a method is disclosed, wherein an olefin is oxidized with molecular oxygen in liquid phase by using an activated supported palladium metal-containing catalyst which has been activated by contacting an olefin having carbon number of 3 to 6 with a supported palladium metal-containing catalyst. In particular, a method is disclosed, wherein a surfactant and an alcohol in Patent Document 2 and a free radical inhibitor in Patent Document 3 are caused to be present in each reaction system, respectively, to improve selectivity to an α,β-unsaturated carboxylic acid. In Patent Document 4, a method is disclosed, wherein a reaction solvent containing a carboxylic acid having carbon number of 2 to 6, tertiary butanol or a ketone having carbon number of 3 to 6 is used. Further, in Patent Documents 1 to 4, there are no descriptions concerning reaction solvents and additives having an acid dissociation exponent (pKa) of less than 4.    Patent Document 1: Japanese Patent Application Laid-Open No. 60-139,341.    Patent Document 2: Japanese Patent Application Laid-Open No. 60-139,643.    Patent Document 3: Japanese Patent Application Laid-Open No. 60-155,148.    Patent Document 4: International Publication No. WO 02/083,299.